reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;

theorem Th67:
  L1 _|_ L2 implies L1 is being_line & L2 is being_line
proof
  assume L1 _|_ L2;
  then consider x1,x2,y1,y2 such that
A1: L1 = Line(x1,x2) & L2 = Line(y1,y2) and
A2: x2 - x1 _|_ y2 - y1;
  y2 - y1 <> 0*n by A2;
  then
A3: y2 <> y1 by Th9;
  x2 - x1 <> 0*n by A2;
  then x2 <> x1 by Th9;
  hence thesis by A1,A3;
end;
